Talanta 76 (2008) 1224–1232

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Optimisation of sensitivity in the multi-elemental determination of83 isotopes by ICP-MS as a function of 21 instrumental operativeconditions by modified simplex, principal component analysis andpartial least squares

Emilio Marengo ∗, Maurizio Aceto, Elisa Robotti, Matteo Oddone, Marco BobbaDepartment of Environmental and Life Sciences, University of Eastern Piedmont, Via Bellini 25/G, 15100 Alessandria, Italy

a r t i c l e i n f o

Article history:Received 11 January 2008Received in revised form 16 May 2008Accepted 21 May 2008Available online 8 June 2008

Keywords:ICP-MS

a b s t r a c t

The optimisation of the sensitivity in the ICP-MS determination of 83 isotopes, as a function of 21 opera-tive parameters was performed by generating an initial experimental design that was used to define, byprincipal component analysis, the multi-criteria target function. The first PC, which contained an overallevaluation of the signal intensity of all isotopes, was used to rank the experiments. The modified simplexoptimisation technique was then applied on the ranked experiments. The increase in signal intensity was,on the average, 3.9 times for the isotopes considered for the simplex procedure. When finally convergencewas achieved, a PLS regression model calculated on the available experiments allowed to investigate the

Modified simplex optimisationMultivariate ranking methodsPP

effect played by each factor on the experimental response. Simplex and PCA proved to be extremely effec-tive to obtain the optimisation and to generate the multi-criteria target function: they can be suggested

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. Introduction

Inductively Coupled Plasma-Mass Spectrometry (ICP-MS) isecoming one of the most widely used techniques for the deter-ination of elements at trace and ultra-trace level (ppb, ppt). The

CP-MS instruments are characterised by a large set of operativearameters which can exhibit various effects on the analyticalesults by influencing the interference pattern, the sensitivity ofhe determination, the time of analysis, etc. These parameters set-ing must be optimised as a function of the specific analysis. As aule of thumb, all instruments do present an auto-tuning procedure,sually based on the One-Variable-At-a-Time (OVAT) approach, toearch for the optimal setting of the operative parameters. TheVAT approach consists in the optimisation of each instrumen-

al parameter independently, to obtain the maximum signal of aelected isotope: this approach therefore does not take into con-ideration the interactions that often exist between the operative

arameters.

Several papers appeared in the nineties about the optimisationf ICP-MS instrumental conditions. Among them, the paper fromord et al. [1] reports the multi-elemental optimisation of plasma

∗ Corresponding author. Tel.: +39 0131 360272; fax: +39 0131 360250.E-mail address: marengoe@tin.it (E. Marengo).

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039-9140/$ – see front matter © 2008 Elsevier B.V. All rights reserved.oi:10.1016/j.talanta.2008.05.052

orm the optimisation of the instrumental operative conditions.© 2008 Elsevier B.V. All rights reserved.

arameters and ion optics in ICP-MS. The simplex procedure waspplied to the optimization of plasma and ion optics parameters.ptimisation was successfully performed on the S/N ratios of 10lements.

Another paper from van Veen et al. [2] reports the optimisa-ion of ICP-MS conditions with respect to short- and long-termrecision. The authors derived an expression of the precision asfunction of the mass intensity in terms of the source flicker and

hot noise contributions.More recently, some more dedicated papers have appeared deal-

ng with the optimisation of the instrumental parameters in ICP-MSy experimental design techniques [1–11]. Brennetot et al. [3]pplied experimental designs to the optimisation of 10 operatingonditions of a Multiple-collector inductively coupled plasma masspectrometry (MC–ICP-MS) for the isotopic analysis of gadolinium.ngle et al. [4] applied a multivariate approach to characterise andptimise the dominant H-2-based chemistries in a hexapole col-ision cell used in ICP-MS: in this case the target function for theptimisation was the S/N ratio. Recently, Gomez-Ariza et al. [5] opti-ised a two-dimensional on-line coupling for the determination

f anisoles in wine using an electron capture detector (ECD) andCP-MS after solid phase micro-extraction – gas-chromatographicSPME-GC) separation, by a chemometric approach: different ICP-

S conditions (forward power, carrier gas flow and the addition ofmall percentages of alternate gases) have been optimised. Other

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pplications of experimental designs to the optimisation of ICP-S analysis are by Gomez-Ariza et al. [5], Darrouzes et al. [6] andartos et al. [7]. In the paper from Darrouzes the optimisation

f ICP-MS equipped with collision/reaction cell (C/RC) technol-gy for the determination of selenium at ultra-trace level. Severalarameters were optimised: gas flow rates for helium and hydro-en and the voltage of the different ionic lenses disposed aroundhe C/RC (quadrupole bias, octopole bias, cell entrance, cell exit,late bias). The paper from Martos et al. is focused instead on there-concentration and determination of Pt; various parameters andhemical variables affecting the preconcentration and determina-ion of this metal by ICP-AES were evaluated. Five variables (sampleow rate, eluent flow rate, nebulizer flow rate, buffer concentrationnd mixing coil length) were considered as factors in the optimi-ation process. Interactions between analytical factors, and theirptimal levels were investigated using two level factorial and cen-ral composite designs. The optimum conditions established werepplied to the determination of platinum by flow injection induc-ively coupled plasma atomic emission spectrometry (FI-ICP-AES).

Optimisation procedures are usually applied to ICP-MS analy-is focusing on a restricted number of instrumental parameters orf elements, according to the scientists’ particular interests; it ismportant to point out however that one of the potentials of ICP-MSnalysis is the possibility of determining a great number of ele-ents contemporarily: this is particularly interesting for routine

nalyses. From this starting consideration, we focused our atten-ion on the contemporary determination of 83 isotopes, in order tobtain experimental conditions representing the best compromiseor the identification of all these isotopes in routine analyses. Due tohe large number of isotopes to be determined, an exhaustive studyf all the instrumental parameters involved is necessary, in order tochieve the best experimental settings. 21 parameters, described inetail in the experimental section, were thus involved in the study.he modified simplex procedure [12–15] was selected to performhe optimisation of the 21 parameters. Simplex represents in thisase the best choice in order to limit the number of experimentseeded to accomplish optimisation: due to the large number of

actors studied, full factorial designs cannot be applied, while frac-ional factorial designs generate complex confounding structuresnd, furthermore, complex variables effects and interactions areossibly expected. The simplex iterative procedure represents thusgood alternative.

The large number of experimental signals to be maximised (the3 isotopes), requires the definition of an effective and suitableulti-criteria target function. Usually the target function adopted

s the sum of all the signals. In this case, the multi-criteria targetunction, representing the signal of almost all the isotopes simul-aneously, was generated by Principal Component Analysis (PCA)16,17]. The initial simplex (22 starting experiments) was used toenerate the multi-criteria target function: PCA was carried outn the signals recorded for the 83 isotopes for the initial pool of2 experiments. This procedure represents a valid alternative dueo the robustness of PCA: considering only the first relevant prin-ipal components (PCs), random variations due to experimentaloise can be eliminated. Once defined the multi-criteria function,he iterative modified simplex method was applied. At each itera-ion each new experiment is projected on the space given by theelevant PCs previously calculated in order to evaluate the finalultivariate experimental response. The iterative simplex allows

o obtain new best settings with respect to the OVAT approach.

he results obtained by the Simplex procedure were compared tohose obtained from the OVAT approach, representing the defaultettings.

Simplex optimisation, however, provides no model relating thenstrumental parameters and the target function. Therefore, a Par-

6 (2008) 1224–1232 1225

ial Least Squares (PLS) [16,17] regression model was built based onhe overall set of experiments performed, to shed light on the effectf each experimental factor on the final response. This model cane used to identify which experimental factors are more importantnd the relationships existing among them.

From an operative point of view, the contemporary optimisationf all the instrumental parameters to obtain the best conditionsor the determination of all the detectable elements representsn important application in routine analyses and could representvalid alternative for default instrumental settings optimisation.ere, the attention is focussed on the proposal of a multivariate pro-edure for the automatic optimisation of the instrumental settingsn ICP-MS.

The present approach represents a valid procedure due to theoupling of simplex optimisation to the establishment of a tar-et function based on principal component analysis: this allowso take into consideration the relationships and the interactionsmong the variables that cannot be taken into account in standardVAT procedures where each variable is optimised independently

rom the others. Moreover, even if the Simplex procedure is stoppedefore achieving convergence, it can provide experimental settingshat are better with respect to the initial ones, due to the itera-ive method applied. This is important when optimisation has toe undertaken with constraints on the maximum time available toerform the optimisation itself.

. Theory

.1. The proposed procedure

The optimisation of the signals of 83 isotopes as function of 21perative parameters in ICP-MS is carried out here by the applica-ion of a procedure consisting in four main steps:

Identification of the initial simplex. The initial set of experiments tobe performed was determined by the simplex procedure [12–15].In the present case 21 operative parameters were studied, thusproviding an initial set of 22 experiments (p + 1 initial experi-ments, where p is the number of factors to be investigated), calledsimplex. The default settings provided by the proprietary softwarepresent on the instrument, were selected as starting conditionsfor the initial simplex. The initial Simplex establishes a startingpool of experiments where the parameters are varied one-at-a-time.Identification of a multivariate target function by Principal Compo-nent Analysis. For each experiment of the initial simplex the signalof the 83 isotopes was recorded. A multivariate target functionwas then identified by applying Principal Component Analysis(PCA) [16,17] on the data recorded from the initial simplex. Ascommonly acknowledged, PCA is a pattern recognition methodrepresenting objects in a new reference system characterised byvariables called Principal Components (PCs). PCs are orthogonalto each other and are computed hierarchically (the informationaccounted for by successive PCs is decreasing): in this way theyaccount for independent sources of information and experimen-tal noise and random variations are contained in the last PCs (theycontain the least possible information). The optimisation of theinstrumental parameters with respect to the simultaneous max-imisation of the signal of all the isotopes (expressed as number ofcounts for each isotope) requires the use of a multi-criteria rank-

ing method: PCA can then be effectively used to this purpose. PCAis then performed on the dataset consisting in the experimentalresponses of the initial pool of experiments and the final targetfunction can be selected by the identification of the PC mostlyrelated to the overall signal increase. This represents a valid alter-

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native to the use of the total sum of the signals of all the isotopesof interest since PCA can effectively separate experimental noisefrom actual systematic information. The optimisation can be per-formed in this case on a more robust target function that takes intoaccount the relationship between the signal of different isotopes.Application of the modified simplex optimisation procedure. Oncethe target function is established, the modified simples optimi-sation procedure can be applied. In the present research we usedthe modified simplex [14] version, in which, during the searchfor the optimum, the simplex changes its shape, assuring a morerapid convergence. It is important to point out that Simplex, beingan iterative procedure, does not guarantees to achieve the globaloptimum but it may converge on local optimal conditions. Thisprocedure is however suitable in the present case characterisedby a large number of parameters to be investigated. At each itera-tion, the experimental responses of the 83 isotopes are projectedon the space given by the PCs selected as multivariate target func-tion and the final multivariate response is then calculated. Onthis multivariate response the simplex optimisation procedure iscarried out. After convergence is achieved, LOD and LOQ are calcu-lated using the optimised instrumental conditions and comparedto those calculated using the default settings.Final refinement by Partial Least Squares regression. The overalldataset consisting in the whole set of experiments performed(initial simplex plus the experiments carried out to accomplishoptimisation) can be used to build a PLS model [16,17] relatingthe 21 operative parameters (X-variables) and the signal of the83 isotopes detected (Y-variables). Since in this case several Y-variables are present, the PLS2 algorithm was used [16,17]. Thismodel can be used for understanding the effect played by eachinstrumental parameter on the signal of each isotope, thus pro-viding information about their effect on different masses.

he procedure adopted represents a interesting method for on-ine optimisation of ICP-MS experimental conditions since it cane completely automated. Moreover, it can be easily implemented

n the instrument software and causes no further time consump-ion with respect to the OVAT approach. Finally, it can also beccomplished by imposing a limiting time consumption: the pro-edure can be stopped at every iteration providing in each stepetter experimental setting with respect to the default ones even

f final convergence is not achieved. It must also be considered thathe simplex optimisation procedure coupled to PCA for providingn adequate multivariate target function takes into considerationhe relationships existing between the variables and among thexperimental responses, that is impossible by the use of the OVATpproach, where correlations are neglected.

. Experimental

.1. ICP-MS analysis

An X5 ICP-MS instrument (Thermo Elemental, Winsford, UK),quipped with an ASX-500 autosampler (CETAC, Omaha, USA)as used for elemental analysis. Data acquisition and process-

ng were performed using the PlasmaLab 2.3 software (Thermolemental, Winsford, UK). The instrumental configuration was var-ed according to Simplex and PLS experiments. The instrumentas tuned daily with a solution containing 10 �g L−1 of Li, Y,e and Tl.

All the reagents used were of analytical purity. Nitric acid usedo acidify the samples before analysis was further purified byub-boiling distillation in a quartz apparatus. Water was puri-ed in a Milli-Q system, resulting in water with a resistivity of8 M�.

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6 (2008) 1224–1232

ICP-MS optimisation through the simplex procedure was per-ormed on standard metal solutions (i.e. no matrix effects norolyatomic interferences were analysed in this first study). Stan-ard metal solutions were prepared from 10 mg L−1 multi-elementtock solutions (Analab, Hoerdt, France). The solution used for Sim-lex procedure was at concentration of 10 �g L−1 for all isotopes.o calculate limits of detection (LOD) and limits of quantificationLOQ) we used 40, 75, 100, 200 and 400 ng L−1 solutions. LOD andOQ were calculated by keeping in due consideration the calibra-ion curves and the signal due to blanks and standards [16–19].

.2. Software

PCA, PLS and graphical representations were performed byedicated software packages: Unscrambler 9.5 (CAMO, Norway),tatistica 7.5 (Statsoft Inc, USA), Excel 2000 (Microsoft Corporation,SA).

.3. Dataset

The optimisation procedure was applied to 21 instrumentalarameters, divided into four main groups with respect to theirurpose: torch-box parameters, related to the position of the torch

n the torch-box (Horizontal, Vertical and Sampling depth); gas-flowarameters (Nebuliser, Cool and Auxiliary); quadrupole and acquisi-ion parameters (Pole bias, Forward power, Standard resolution, Dwellime, Sweeps, Channel); focusing parameters. This last group con-ists in 9 parameters related to the position of lenses and deflectorsf the ion flow. Extraction is related to the first lens, located in theion transfer system”, which avoids dispersion of ions into the vac-um chamber and speeds them up towards the system. Lens 1, 2 andretain negative ions or neutral species. D1, D2, DA act as deflectorsf the ionic flow retaining photons generated from plasma fromeaching the detector (thus increasing the baseline noise). Focuscts on particle dispersion into the “ion transfer system”. Hexapoleias acts on the reduction of the interferences due to polyatomicpecies.

. Results and discussion

.1. Initial simplex and multi-criteria target function

The simplex procedure was applied to the optimisation of the1 instrumental parameters previously described. The default set-ings (selected according to an OVAT approach), provided by theroprietary software present on the instrument, were selected astarting conditions for the simplex procedure. The default settingsnd the variations applied to each factor are reported in Table 1,hile the initial 22 experiments are listed in Table 2. As just pointed

ut, the initial Simplex establishes a starting pool of experimentshere the parameters are varied one-at-a-time. The initial simplexas the double purpose of identifying a suitable multivariate tar-et function (by the application of PCA) and providing the startingoint for the subsequent optimisation procedure by the modifiedimplex algorithm.

In order to establish an appropriate target function, PCA waserformed on the dataset constituted by the initial simplex, afterutoscaling. The dataset thus consists in 22 experiments describedy the 83 signals of the isotopes detected. From an operative pointf view, the choice of a target function based on the overall signals

f the isotopes could not be the best alternative since the optimi-ation of signals due to interferences is simultaneously considered.his choice was justified in our case, since the large number of iso-opes to be monitored did not allow the simultaneous monitoringf all interfering species together in a reasonable time of analysis.

E. Marengo et al. / Talanta 76 (2008) 1224–1232 1227

Table 1Default settings (selected as starting conditions for the simplex procedure), the variations applied to each factor and the optimal settings obtained from the simplex procedure(corresponding to exp. 119)

Default Variation Simplex optimal settings

Sweeps 25 50 37Dwell time 10 50 39Channels 3 2 1Standard res 125 25 111Extraction −200 50 −240Lens 1 −2.3 20 −14.0Lens 2 −57.2 40 −45.2Lens 3 −112.9 20 −106.2Focus 28.1 5 23.6Horizontal 45 15 57Vertical 425 80 340Sampling depth 90 60 66Nebuliser 0.92 0.05 0.92D1 −26.6 10 −27.2D2 −145 40 −127.5DA −146.6 20 −146.9Pole bias 6.5 2 1.7HCAF

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exapole bias −4.9ool 13.1uxiliary 0.9orward power 1310

oreover, the increase of the signal recorded setting up experi-ental parameters cannot reasonably be completely ascribed to

n increase of the interferences: isotopic signals will be increaseds well. This compromise can be acceptable if interferences are kept

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n due consideration in a subsequent step, once a restricted pool ofarget isotopes, to be detected in a particular sample, are identified.

valid alternative should be the used of S/N ratios but the choicedopted in the present case does not invalidate the overall proce-

of PC1 (a) and PC2 (b) and score plot (c) for the first two PCs.

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ure since the a posteriori calculation of LODs and LOQs states thatn overall improvement is achieved, as will be widely documentedfterwards.

The first two PCs calculated were then retained as significant,ince they account for more than 97% of the total variance (86%C1, 11% PC2). The score plot and loading plot of the first two PCs areepresented in Fig. 1. The loadings of PC1 and PC2 are representedeparately as bar diagrams, reporting the variables on the x-axisnd the loadings on the y-axis.

Looking at the loading plot (Fig. 1(a) and (b)), the first compo-ent shows positive loadings for all the isotopes. However, isotopesith intermediate mass values show the largest positive loadings

nd lay along the first component, while isotopes characterised bymall and large masses have, respectively, large positive and largeegative loadings on the second component. For what regards PC1,

n anomalous weight can be detected for 43Ca, showing a valuemaller than that of near isotopes. An anomalous behaviour can beetected for 7Li and 23Na as well, on the second PC: 7Li shows amaller weight on PC2 with respect to that of the isotopes with aimilar mass, while 23Na shows a weight around 0, where a posi-

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able 2he initial Simplex experimental conditions

o. Sweeps Dwell time Channels Std Res Extract1 2 3 4 5

1 25 10 3 125 −2002 67 16 3 128 −1943 31 52 3 128 −1944 31 16 5 128 −1945 31 16 3 146 −1946 31 16 3 128 −1587 31 16 3 128 −1948 31 16 3 128 −1949 31 16 3 128 −194

10 31 16 3 128 −19411 31 16 3 128 −19412 31 16 3 128 −19413 31 16 3 128 −19414 31 16 3 128 −19415 31 16 3 128 −19416 31 16 3 128 −19417 31 16 3 128 −19418 31 16 3 128 −19419 31 16 3 128 −1940 31 16 3 128 −194

21 31 16 3 128 −1942 31 16 3 128 −194

o. Vertical Sampling depth Nebuliser D1 D2 DA11 12 13 14 15 16

1 425 90 0.92 −26.6 −145 −146.2 435 97 0.93 −25.4 −140 −144.3 435 97 0.93 −25.4 −140 −144.4 435 97 0.93 −25.4 −140 −144.5 435 97 0.93 −25.4 −140 −144.6 435 97 0.93 −25.4 −140 −144.7 435 97 0.93 −25.4 −140 −144.8 435 97 0.93 −25.4 −140 −144.9 435 97 0.93 −25.4 −140 −144.

10 435 97 0.93 −25.4 −140 −144.11 435 97 0.93 −25.4 −140 −144.12 492 97 0.93 −25.4 −140 −144.13 435 140 0.93 −25.4 −140 −144.14 435 97 0.96 −25.4 −140 −144.15 435 97 0.93 −18.3 −140 −144.16 435 97 0.93 −25.4 −112 −144.17 435 97 0.93 −25.4 −140 −130.18 435 97 0.93 −25.4 −140 −144.19 435 97 0.93 −25.4 −140 −144.0 435 97 0.93 −25.4 −140 −144.

21 435 97 0.93 −25.4 −140 −144.2 435 97 0.93 −25.4 −140 −144.

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ive value is expected. On the whole, PC1 mainly accounts for theverall signal intensity, since all variables present positive loadingsn this PC. This behaviour is possible even if data are autoscaled,ince the first PC accounts for the overall signal increase. The secondC is instead responsible for the information about the elementalass: large negative loadings for isotopes with large masses, large

ositive loadings for isotopes with small masses. For the optimi-ation of the instrumental settings, a target function related to theverall increasing instrumental signal was needed, the choice washerefore the first PC: large PC1 values will then be searched for,orresponding to large overall signals.

Looking at the corresponding score plot (Fig. 1(c)), experimentst positive values on PC1 correspond to experiments showing anncrease of all the signals simultaneously, while experiments ategative values present a decrease of all the isotopes signal. Mov-

ng along the first PC towards more positive values therefore meansoving towards higher instrumental signals; this is particularly

rue for the isotopes showing intermediate masses (larger positiveoading), rather than for isotopes with low or high masses (smallerositive loadings).

ion Lens 1 Lens 2 Lens 3 Focus Horizontal6 7 8 9 10

−2.3 −57.2 −112.9 28.1 450.2 −52.2 −110.4 28.7 470.2 −52.2 −110.4 28.7 470.2 −52.2 −110.4 28.7 470.2 −52.2 −110.4 28.7 470.2 −52.2 −110.4 28.7 47

14.3 −52.2 −110.4 28.7 470.2 −23.9 −110.4 28.7 470.2 −52.2 −96.3 28.7 470.2 −52.2 −110.4 32.3 470.2 −52.2 −110.4 28.7 570.2 −52.2 −110.4 28.7 470.2 −52.2 −110.4 28.7 470.2 −52.2 −110.4 28.7 470.2 −52.2 −110.4 28.7 470.2 −52.2 −110.4 28.7 470.2 −52.2 −110.4 28.7 470.2 −52.2 −110.4 28.7 470.2 −52.2 −110.4 28.7 470.2 −52.2 −110.4 28.7 470.2 −52.2 −110.4 28.7 470.2 −52.2 −110.4 28.7 47

Pole bias Hexapole bias Cool Auxiliary Forward power17 18 19 20 21

6 6.5 −4.9 13.1 0.90 13101 6.7 −4.8 13.2 0.91 13201 6.7 −4.8 13.2 0.91 13201 6.7 −4.8 13.2 0.91 13201 6.7 −4.8 13.2 0.91 13201 6.7 −4.8 13.2 0.91 13201 6.7 −4.8 13.2 0.91 13201 6.7 −4.8 13.2 0.91 13201 6.7 −4.8 13.2 0.91 13201 6.7 −4.8 13.2 0.91 13201 6.7 −4.8 13.2 0.91 13201 6.7 −4.8 13.2 0.91 13201 6.7 −4.8 13.2 0.91 13201 6.7 −4.8 13.2 0.91 13201 6.7 −4.8 13.2 0.91 13201 6.7 −4.8 13.2 0.91 13200 6.7 −4.8 13.2 0.91 13201 8.2 −4.8 13.2 0.91 13201 6.7 −4.1 13.2 0.91 13201 6.7 −4.8 13.5 0.91 13201 6.7 −4.8 13.2 0.94 13201 6.7 −4.8 13.2 0.91 1377

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Experiment 1, corresponding to the default settings (Table 2),hows quite good instrumental conditions (large value on PC1) butt performs better for large mass isotopes (large negative value onC2). Experiment 14 is the best one, since it shows the largest posi-ive score on PC1 but it shows a larger signal for small masses thanor large ones; it corresponds to an increase of all the parametersith respect to the default settings, with particular regard to the

ariable “nebuliser”. The position of Experiment 14 in the score plotuggests a quite different behaviour from the other samples: how-ver, this was not detected as an outlier and it was retained in PCAalculation.

From the point of view of the multivariate target function iden-ified as the first PC, the worst experiment is experiment number, showing the smallest score on PC1: this experiment will be therst to be re-projected during the optimisation procedure.

.2. Simplex procedure

Once obtained the multi-criteria target function necessary toccomplish the optimisation procedure, a modified simplex proce-ure [14] was applied for the optimisation of the 21 experimental

actors. Convergence was achieved after 128 iterations, leading tototal of 150 experiments. At each iteration, the worst sample (thene showing the largest negative score on PC1) is selected ande-projected with respect to the centroid of the others. The newxperiment is projected on the space given by the first two PCsreviously calculated to provide the final multivariate experimen-al response in terms of the score of the experiment on PC1. The newxperiment replaces the selected one in the experimental plan if ithows a better result (a less negative score on PC1).

The 150 experiments performed are represented in the spacef the first two PCs in Fig. 2: the experiments belonging to theriginal simplex are represented as squares (they are containedn the ellipse drawn in the figure), while the new projections areepresented as triangles. As expected, the new experiments moveowards larger positive values on PC1, but in the meantime, largerositive values on PC2 are reached. So, the new experiments showlarger signal for all isotopes but in particular for those with smallass values. This is probably due to a major removal of polyatomic

nterferences for small mass isotopes.The experimental settings corresponding to the best conditions

btained by the Simplex procedure are reported in Table 1 (cor-

esponding to experiment no. 119). Table 3 reports the signalsbtained for some of the selected isotopes expressed as number ofounts: the signal registered after the simplex procedure improvedn the average 3.9 times with respect to the default settings; asxpected, the improvements were recorded for small mass isotopes.

ig. 2. Representation of the 150 experiments performed on the space of the firstwo PCs.

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he improvements by far the largest were obtained for 51V and 52Cr.or what regards precision (standard deviation calculated from 5enuine replicates of a standard solution at 100 ng L−1), with theefault settings the average precision is 10%, while it improves tobout 5% with the simplex optimised conditions. Good linearity waschieved for all the revealed isotopes.

Table 3 reports also the LOD and LOQ values calculated by these of the calibration curve for some of the considered isotopes,electing the instrumental tuning according to experiment no. 119.alues inferior to 1 indicate that the corresponding optimisationrocedure produced a worse result with respect to the defaultettings. After performing the Simplex procedure, the sensitivitymprovement was, on the average, 2 times. The best LOD and LOQmprovements were obtained, as expected, with light isotopes (5.97imes for arsenic, 5.15 times for cobalt).

The experimental conditions obtained for experiment no. 119re thus the best settings achieved through the simplex procedure.t is important to point out that the presence of the variable dwellime in the group of variables to be tuned could be a problem ifhe target function is based on the overall number of counts, inact obviously increasing dwell time corresponds to an increase ofhe number of counts; however, the best settings obtained provehat this variable is not so driving since it is settled at intermediatealues.

.3. Partial least squares

PLS can be used in this case to provide a model relating the1 experimental parameters (X-variables) to the 83 experimen-al responses (Y-variables). This analysis, rather than providing auantitative predictive model, is used here to sum up the effectlayed by each experimental factor on the signals of the selected

sotopes. The complete experimental matrix, consisting of 150 rowsthe experiments) and 104 columns (83 columns representing theignal of each isotopes and further 21 columns representing thexperimental settings of each parameter) was used to calculatePLS model. This model was calculated to obtain a quantitative

elationship between the 21 instrumental settings (X-variables)nd the 83 experimental responses (Y-variables). Since our aimas the achievement of a unique model relating the signal of

ll the isotopes together to the experimental settings, the PLS2ethod [16,17] was selected. Data were autoscaled before perform-

ng PLS.The first two latent variables account for about 50% and 81%

f the total variance contained in the X- and Y-variables, respec-ively, and they were considered as significant in the successivenalysis.

The regression coefficients of the PLS2 model, built with the firstwo latent variables on both X- and Y-variables, are representedn Fig. 3. The graphical representation reports the instrumen-al parameters on the y-axis and the isotopes on the x-axis; theegression coefficients for each parameter for each isotope are rep-esented on a colour scale from blue to red: increasing blue tonesorrespond to increasing negative coefficients, while increasing redones correspond to increasing positive coefficients. Coefficientsepresented as white tones are characterised by values around zero,hich do not play a relevant role on modelling the experimen-

al responses. This representation allows a clearer identification ofhe parameters which have to be increased or decreased in ordero optimise the signal of isotopes of interest. The parameters can

e divided in three main groups according to the behaviour ofheir coefficients towards small or large isotopic masses: positiveoefficients for all isotopic masses (Fig. 3, first five parameters),egative coefficients for all isotopic masses (Fig. 3, from focus touxiliary), different positive/negative coefficients for small/large

1230 E. Marengo et al. / Talanta 76 (2008) 1224–1232

Table 3Signal intensities of some of the selected isotopes obtained for the standard 100 ng L−1, corresponding LOD and LOQ values expressed as ng L−1 and signal and LODimprovements with the default and the simplex optimised experimental conditions

Default Simplex Signal improvementa LOD improvementb

Mean signal Dev. std LOD LOQ Mean signal Dev. std LOD LOQ

51V 45.33 8.33 78.90 118.35 429.44 8.03 19.48 29.21 9.47 4.0552Cr 75.11 10.69 46.42 69.62 913.65 6.40 30.38 45.57 12.16 1.5355Mn 104.00 5.33 55.78 83.67 833.03 18.02 26.44 39.66 8.01 2.1159Co 50.22 3.85 65.51 98.26 343.27 20.75 12.72 19.08 6.84 5.1569Ga 61.33 7.42 40.85 61.28 305.16 2.62 13.12 19.68 4.98 3.1172Ge 19.11 1.54 48.50 72.75 117.12 17.92 47.70 71.55 6.13 1.0275As 39.56 14.13 321.07 481.60 149.00 12.84 53.79 80.68 3.77 5.9785Rb 103.56 7.70 30.96 46.44 683.56 10.38 24.52 36.79 6.60 1.2688Sr 280.45 21.72 70.92 106.38 1201.74 32.77 41.66 62.49 4.29 1.7089Y 141.78 3.36 30.24 45.36 589.76 11.58 16.93 25.39 4.16 1.7990Zr 78.67 12.22 58.43 87.65 384.62 18.18 33.14 49.72 4.89 1.7693Nb 121.33 6.93 47.04 70.55 517.46 20.73 15.12 22.68 4.26 3.1195Mo 29.33 4.00 77.34 116.01 94.48 6.21 44.29 66.43 3.22 1.75101Ru 32.00 4.81 102.37 153.56 101.41 12.40 22.62 33.93 3.17 4.53103Rh 1905.09 106.02 16.97 25.46 7217.23 168.74 8.19 12.28 3.79 2.07105Pd 42.67 8.33 67.25 100.88 145.07 15.44 27.21 40.82 3.40 2.47107Ag 68.89 0.77 59.21 88.82 268.89 26.54 57.50 86.24 3.90 1.03111Cd 20.44 2.04 54.95 82.42 78.54 15.72 37.44 56.16 3.84 1.47118Sn 59.11 7.34 61.92 92.88 219.68 5.23 25.91 38.87 3.72 2.39121Sb 79.11 4.68 63.79 95.69 289.22 7.47 14.54 21.80 3.66 4.39125Te 1.78 0.77 157.73 236.60 15.71 2.23 103.00 154.50 8.84 1.53133Cs 141.33 10.91 27.47 41.20 676.16 10.05 16.93 25.40 4.78 1.62137Ba 92.45 1.54 262.34 393.50 326.18 19.43 248.89 373.34 3.53 1.05139La 210.67 26.23 37.24 55.86 783.82 28.89 17.20 25.81 3.72 2.16140Ce 324.01 24.33 75.57 113.36 1103.79 30.51 54.20 81.30 3.41 1.39141Pr 266.23 30.71 18.91 28.36 943.45 12.79 14.12 21.18 3.54 1.34146Nd 56.89 10.78 54.94 82.41 172.33 10.10 21.37 32.06 3.03 2.57147Sm 52.44 6.71 49.46 74.19 152.46 5.00 29.01 43.51 2.91 1.71153Eu 201.34 22.19 20.34 30.50 582.60 35.62 11.61 17.42 2.89 1.75157Gd 60.89 10.36 40.86 61.29 174.87 17.43 23.29 34.93 2.87 1.75159Tb 422.68 8.74 12.53 18.80 1195.97 23.65 14.97 22.45 2.83 0.84163Dy 98.67 10.07 22.48 33.72 313.93 12.26 18.18 27.27 3.18 1.24165Ho 448.01 7.42 15.38 23.08 1190.19 16.29 16.04 24.06 2.66 0.96166Er 143.56 6.71 24.20 36.30 403.57 14.04 13.96 20.95 2.81 1.73169Tm 471.12 34.11 13.67 20.50 1220.92 58.02 17.63 26.44 2.59 0.78172Yb 105.78 7.70 40.21 60.31 280.44 3.82 31.93 47.90 2.65 1.26175Lu 541.35 30.14 11.94 17.91 1322.34 22.81 14.22 21.32 2.44 0.84178Hf 132.89 4.07 30.40 45.60 336.11 29.95 31.79 47.69 2.53 0.96181Ta 623.13 28.01 22.10 33.14 1443.64 46.62 17.96 26.95 2.32 1.23182W 154.22 7.58 32.80 49.21 367.07 20.89 22.73 34.09 2.38 1.44185Re 159.56 16.07 37.77 56.65 424.59 13.01 18.51 27.77 2.66 2.04193Ir 288.89 23.41 24.73 37.10 627.42 15.95 16.17 24.25 2.17 1.53195Pt 98.22 7.34 41.72 62.58 215.06 6.59 16.88 25.32 2.19 2.47205TI 321.34 15.38 28.15 42.23 718.44 11.81 9.65 14.48 2.24 2.92208Pb 327.12 17.91 14.44 21.66 792.83 11.15 14.69 22.03 2.42 0.98209Bi 606.69 35.51 67.63 101.45 1192.04 30.30 31.75 47.62 1.96 2.13232Th 716.92 58.43 36.01 54.02 1445.48 34.21 13.23 19.84 2.02 2.72238U 553.35 23.10 13.80 20.70 1143.52 46.09 16.61 24.91 2.07 0.83

mfindal

(sos(pop

mdasCn

mioe

a As calculated from ratio MeanSimplex/MeanDefault.b As calculated from ratio LODDefault/LODSimplex or LOQDefault/LOQSimplex.

ass elements (last four parameters). Looking at Fig. 3, the firstour parameters show positive or almost null coefficients for all thesotopic masses: an increase of these parameters increases the sig-al of the investigated isotopes. In particular, an increase of D2 andwell time increases prevalently the signal of small masses whilen increase of forward power and nebuliser improves the signal ofarge masses.

For what regards negative coefficients, the first six parametersfrom focus to standard resolution) provide an increase of the overallignals when they are decreased. DA, lens 3 and cool act prevalentlyn large mass isotopes (they have to be decreased to record a larger

ignal), while lens 1, sweeps and auxiliary act on small mass isotopesthey have to be decreased to record a larger signal). The last fourarameters show a different behaviour with respect to their effectn the signal of small and large mass isotopes: channels and D1 showositive coefficients for large masses and negative ones for small

te

rs

asses (they have to be increased to improve large masses andecreased to improve small masses); lens 2 and hexapole bias shown opposite behaviour, so they have to be increased to improvemall masses and decreased to improve large masses. However,hannels and hexapole bias show the smallest coefficients and areot particularly relevant to the regression model built.

Fig. 3 thus allows to sum up the effects played by each instru-ental parameter on the signal recorded for the investigated

sotopes: looking at this representation it is therefore possible tobtain different optimal experimental conditions according to thelements of interest. In fact, it allows the definition of a quantita-

ive mathematical model relating the signal of each isotope to thexperimental settings.

The effects played by each factor on the final experimentalesponse pointed out so far are obviously characteristic for thispecific case. However, some of the parameters analysed are of

E. Marengo et al. / Talanta 76 (2008) 1224–1232 1231

F ariabler

gicneoeatafncpa

5

iTcoiybttulimwpasb

dTmf

eil8aitdstfie

wo

asta

tap

R

ig. 3. Regression coefficients of the PLS2 model built with the first two latent vepresented on the y- and x-axes respectively.

eneral interest in ICP-MS optimisation, since they are universallymportant in ICP-MS determinations (e.g. gas flow, torch position,hannels, resolution, etc.). Anyway, the present application doesot focus on the identification of the particular role played byach factor on the selected isotopic masses but on the potentialf multivariate optimisation tools for the achievement of optimalxperimental settings in cases where a large number of parametersnd experimental responses have to be taken into account. Fromhis point of view, this application proves that multivariate tools,s Simplex coupled to PCA to identify a suitable target function, per-orm well in the identification of optimal settings providing largerumber of counts and better LOD and LOQ values with respect toommon optimisation tools based on the OVAT procedure generallyresent in software packages. This procedure could thus representvalid alternative for routine analyses.

. Conclusions

21 experimental parameters were optimised with respect to thencreasing sensitivity of the ICP-MS determination of 83 isotopes.he innovation of the proposed approach is represented by theontemporary optimisation of the 21 instrumental parameters tobtain the best settings for the determination of all the detectablesotopes together. The procedure is interesting for routine anal-ses where a great number of elements have to be determined,ut it can be also exploited by companies as a valid alternativeo the OVAT approach, for proposing default optimal instrumen-al settings. In particular, the simplex procedure, coupled to these of a multivariate target function selected by PCA, is particu-

arly effective since it takes into consideration the relationships andnteractions among the experimental parameters and the experi-

ental responses: this is impossible exploiting an OVAT approach

here each variable is considered separately. Moreover, the sim-lex procedure can be applied to achieve convergence but it canlso be applied considering a limited time consumption: after aelected time period dedicated to optimisation the procedure cane stopped and the final best settings can be used as optimised con-

s on both x- and y-variables. The instrumental parameters and the isotopes are

itions providing in any case an improvement of the final response.he applied procedure can be easily implemented in the instru-ent software, thus providing a completely automated procedure

or optimisation.For what regards the present application, an initial set of 22

xperiments was performed according to a starting simplex involv-ng the variation of one parameter at a time (Table 2). Due to thearge number of signal intensities to be maximised (for the overall3 isotopes), the set of 22 experiments was used to choose a suit-ble multi-criteria target function, accounting for the overall signalntensity of all the isotopes to be determined. The best target func-ion was selected as the first PC calculated performing a PCA on theataset given by the first 22 experiments. The subsequent modifiedimplex optimisation procedure was then carried out maximisinghe target function (i.e. the positive score of the experiments on therst PC) and it reached convergence after 128 iterations (150 totalxperiments).

The best experimental conditions obtained by this procedureere further investigated through a PLS2 model, relating the signal

f the 83 isotopes to the experimental settings.The increase in signal intensity was on average 3.9 times. LOD

nd LOQ were calculated for the default settings and for the optimalettings obtained by the Simplex procedure: the increase in sensi-ivity obtained from the simplex optimised conditions was, on theverage, 2 times, with a maximum of 5.97 times for arsenic.

The final PLS also allows to obtain a mathematical model relatinghe instrumental parameters to the experimental responses, thusllowing to sum up the information about the role played by eacharameter in influencing the isotopes number of counts.

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